A 2000 kg truck traveling due north 10 m/s is hit
by a 1200 kg car driven by a crazy driver traveling due east 25 m/s
out of a side street. The two interlock. Calculate the
velocity of the combined wreck, including the magnitude and
direction. Ignore friction.
conserve momentum
2000(10j) + 1200(25i) = (2000+3200)(xi+yj)
20,000i + 30,000j = 5200(xi+yj)
x = 200/52 = 3.85
y = 300/52 = 5.77
so v = 3.85i + 5.77j
|v| = 6.93
tanθ = 5.77/3.85 = 56.28°
so, final v is
6.93 m/s @ N 33.71° E